Computation of Boltzmann Model Equation Using Asymptotic-Preserving and WENO Scheme
Date Issued
2014
Date
2014
Author(s)
Kang, Wei-Yi
Abstract
An accurate and direct algorithm for solving the classical Boltzmann equation and the semiclassical Boltzmann equation with relaxation time approximation in phase space is presented for parallel treatment of rarefied gas flows of particles of three statistics. In time domain, we use asymptotic-preserving method for solving two-dimensional Riemann problem by the classical Boltzmann equation and the semiclassical Boltzmann equation with very small relaxation time. After using asymptotic-preserving, we use fourth-order Runge-Kutta method to discrete time domain. In space domain, we use fifth-order weighted essentially non-oscillatory scheme to evolve the flux term. The discrete ordinate method is applied to remove the microscopic velocity dependency of the distribution function that renders the Boltzmann BGK equation in phase space to a set of hyperbolic conservation laws with source terms in physical space. Computational examples of two-dimensional Riemann problems for rarefied gas flows at very small relaxation time are presented. By using WENO scheme, the results show good resolution in capturing the main flow features while using grids with few good points.
Subjects
直接解法
古典波茲曼模型方程式
波茲曼方程式
半古典橢球波茲曼模型方程式
加權基本不震盪算則
分立坐標法
漸近保守算則
Type
thesis
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